Nigel Higson and John Roe Abstract: We connect the assembly map in C∗-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani’s theorem that whenever the C∗-algebra assembly map is an isomorphism, the relative eta invariants associated to the signature operator are ho...

In this paper, we investigate the Fourier coefficients of eta-quotients forms q λ 0 + l k 1 24 η ( τ ) − , $$ {q}^{\frac{\lambda_0+{l}^k{\lambda}_1}{24}}\eta {\left(\tau \right)}^{-{\lambda}_0}\eta {\left({l}^k\tau \right)}^{-{\lambda}_1}, where \eta \left(\tau \right) is Dedekind eta function, = 5,7 11 13 l=5,7,11,13 and 17; a positive integer, {\lambda}_0,{\lambda}_1 are arbitrary integers. W...

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent lambda . An oscillator of degree k_{i} is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of Jk_{i};{eta-1} . By invoking the mean-field approach, we find eight different synchronization transition beha...

To characterize the function of the CD3 eta subunit of the T cell receptor (TCR), we have used cDNAs encoding CD3 zeta, CD3 eta, or both to reconstitute a variant of a cytochrome c-specific, I-Ek-restricted murine T cell hybridoma, termed MA5.8, which lacks CD3 zeta and CD3 eta proteins. We provide direct evidence that assembly and surface expression of TCRs can be mediated by either of these s...

The eta-subunit of the TCR is derived from an alternative splice product of the TCR-zeta gene. The eta-subunit has been extensively characterized in murine T cells, where up to 10% of TCR bear zeta-eta heterodimers rather than zeta-homodimers. In contrast to the significant levels of eta found in murine T cells, in human PBL an eta-like region is expressed spliced to upstream exons of the zeta-...

Endothelin is a vasoconstricting peptide that plays a key role in vascular homeostasis, exerting its biologic effects via two receptors, the endothelin receptor A (ETA) and endothelin receptor B (ETB). Activation of ETA and ETB has opposing actions, in which hyperactive ETA is generally vasoconstrictive and pathologic. Selective ETA blockade has been shown to be beneficial in renal injuries suc...

in this paper, we first introduce the notion of $c$-affine functions for $c> 0$.then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. moreover, a hyers–-ulam stability result for strongly convex functions is shown.

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...